prove that √p+√q is irrational where pq are primes
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Let us suppose that √p + √q is rational.
Let √p + √q = a, where a is rational.
=> √q = a – √p
Squaring on both sides, we get
q = a2 + p - 2a√p
=> √p = (a2 + p - q)/2a, which is a contradiction as the right hand side is rational number, while √p is irrational.
Hence, √p + √q is irrational.
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Similar questions
Let √p + √q is rational number
A rational number can be writeen in the form of a/b
so
√p + √q = a/b
√p = a/b _ √q
√p = ( a - b √ q ) /b
P, Q are integers then ( a - b √Q ) /b
it is a rational number
So √p is also rational number
So it contradicts that √p + √Q is irrational number
So it is s false that it is irrational number
it is a rational number √p
hope it helps
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